Question

2sinA-sin2A÷2sinA+sin2A=

Answer 1

Hi,

Here is your answer !
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$\frac{2 \sin A - \sin 2A}{2 \sin A + \sin 2A} \\ \\ = \frac{2 \sin A - 2 \sin A \cos A}{2 \sin A + 2 \sin A\cos A} \\ \\ = \frac{2 \sin A(1 - \cos A)}{2 \sin A(1 + \cos A)} \\ \\ = \frac{1 + \cos A}{1 - \cos A} \\ \\ = \frac{ 2 \cos ^{2} ( \frac{A}{2})}{2 \sin ^{2} ( \frac{A}{2}) } \\ \\ = \cot ^{2} (\frac{A}{2})$

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IDENTITY USED :
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★ sin2θ  = 2sinθ cosθ 
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★ cos2θ  = 1 - 2sin²θ 

=> 1 - cos2θ  = 2sin²θ 
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★ cos2θ  = 2cos²θ  - 1

=> 1 + cos2θ  = 2cos²θ 
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★ cotθ = cosθ / sinθ 

Answer 2

Step-by-step explanation:

Question :prove 2sinA-sin2A÷2sinA+sin2A=tan²A÷2